Precalculus Examples

$f (x) = \log_{7} (11 x + 3)$

Step 1

Set the argument in $\log_{7} (11 x + 3)$ greater than $0$ to find where the expression is defined.

$11 x + 3 > 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $3$ from both sides of the inequality.

$11 x > - 3$

Step 2.2

Divide each term in $11 x > - 3$ by $11$ and simplify.

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Step 2.2.1

Divide each term in $11 x > - 3$ by $11$ .

$\frac{11 x}{11} > \frac{- 3}{11}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $11$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{11 x}{11} > \frac{- 3}{11}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 3}{11}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Move the negative in front of the fraction.

$x > - \frac{3}{11}$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \frac{3}{11}, \infty)$

Set-Builder Notation:

${x | x > - \frac{3}{11}}$

Step 4